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arXiv:2311.17229

A nonlinear frequency shift caused by asymmetry of the coherent population trapping resonance: a generalization

Eugene A. Tsygankov, Dmitry S. Chuchelov, Maria I. Vaskovskaya, Vitali V. Vassiliev, Sergei A. Zibrov, Vladimir L Velichansky

Published Nov 28, 2023• 0 citations
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Abstract

We investigate the coherent population trapping resonance induced by a polychromatic optical field with an asymmetric spectrum, i.e., whose sidebands equidistant from the carrier have unequal powers. A situation is considered where a modulation is used to provide the so-called in-phase and quadrature signals in the optical field's transmission, which are used for stabilization of the local oscillator's frequency in chip-scale atomic clocks. In a general case, the frequencies of the signals nonlinearly depend on the optical field's intensity due to the asymmetry of the resonance. In this work, we demonstrate a) that this effect stems from a multi-peak structure of the resonance; b) a linear dependence of the frequency on the optical field's intensity at high modulation values; c) that the regime of the resolved structure has more advantages than suppression of the frequency shift due to the spectrum asymmetry.

DOI
10.48550/arxiv.2311.17229

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Comment on “Light Shifts of Coherent Population Trapping Resonances in a Periodically Modulated Laser Field” (JETP Letters 122, 139 (2025))

Eugene A. Tsygankov

In this comment, I demonstrate that an addition to the light shift of the coherent population trapping resonance’s frequency, shown in [V. I. Yudin, M. Yu. Basalaev, A. V. Taichenachev, O. N. Prudnikov, M. D. Radchenko, and V. G. Palchikov, JETP Lett. 122, 144 (2025)], is not due to a new physical effect but is consequence of the asymmetry. To do this, the following model is considered. The phase of a monochromatic optical field is harmonically modulated at the frequency corresponding to the interval between ground-state levels of the Λ-scheme. The carrier is tuned to the low-frequency transition, while the first-order sideband is resonant to the high-frequency transition. I present curves demonstrating the opposite asymmetry of the resonance for the cases of the shift deviating from the light one in different directions.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 2026•0 citations
We investigate the coherent population trapping resonance induced by a polychromatic optical field with an asymmetric spectrum, i.e., whose sidebands equidistant from the carrier have unequal powers. A situation is considered where a modulation is used to provide the so-called in-phase and quadrature signals in the optical field's transmission, which are used for stabilization of the local oscillator's frequency in chip-scale atomic clocks. In a general case, the frequencies of the signals nonlinearly depend on the optical field's intensity due to the asymmetry of the resonance. In this work, we demonstrate a) that this effect stems from a multi-peak structure of the resonance; b) a linear dependence of the frequency on the optical field's intensity at high modulation values; c) that the regime of the resolved structure has more advantages than suppression of the frequency shift due to the spectrum asymmetry.
We study the coherent population trapping resonance induced by the radiation of a microwave-current-modulated diode laser. The situation is considered when a harmonic phase modulation of the microwave field is used to generate the error signal for the frequency stabilization of atomic clocks. We demonstrate that in this case the resonance acquires a multipeak structure. If it is asymmetric and the components of the multipeak structure are not fully resolved, then the resonance frequency nonlinearly depends on the laser field intensity. The peaks become separated at an increase in the frequency of the phase modulation, providing a linear dependence of the frequency on the intensity of the laser field. This theoretical prediction is confirmed experimentally. Other advantages of the high-frequency modulation regime are also discussed.
We theoretically study the frequency shift in atomic clocks caused by the line-shape asymmetry of coherent population trapping (CPT) resonance in a bichromatic laser field. This asymmetry arises due to the inequality of the resonant spectral components and nonzero one-photon detuning. The line-shape-asymmetry-induced shift depends on the intensity of the resonant fields, which leads to a degradation in long-term stability due to fluctuations of the laser field parameters. A frequency stabilization based on the harmonic modulation of two-photon detuning is considered. It is shown that the use of a high-frequency modulation (compared to the CPT resonance width, i.e., the Pound-Drever-Hall regime) makes it possible to significantly suppress this shift (by one to two orders of magnitude).
We have found that the error-signal frequency corresponding to the coherent population trapping resonance can be displaced from that of "0−00-00−0" transition unperturbed by the optical field, although the frequency is not sensitive to changes in its intensity. We consider the double ΛΛΛ-system of levels interacting with the asymmetric polychromatic optical field to demonstrate that this effect arises due to intensity nonlinearity of the error-signal frequency shift. The experiment with 87^{87}87Rb atoms in Ar-N2_22​ buffer gas atomic cell shows how the displacement value depends on different parameters. The possible influence of the effect on the clocks' frequency stability and reproducibility are discussed.
The appearance of the population difference in the ground state of the Λ\Lambda Λ -system due to the spontaneous decay of the upper level into lower ones is considered. The resulting asymmetry of the coherent population trapping resonance is shown to lead to a frequency shift of the quadrature signal, which nonlinearly depends on the optical field intensity. In this case, this contribution is not suppressed due to the use of high modulation frequencies compared to the relaxation rate of ground state polarization (analogue of the Pound–Drever–Hall technique). A significant smallness of this shift when using a binary mixture of noble buffer gases is discussed.
We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.
In this comment, I demonstrate that an addition to the light shift of the coherent population trapping resonance’s frequency, shown in [V. I. Yudin, M. Yu. Basalaev, A. V. Taichenachev, O. N. Prudnikov, M. D. Radchenko, and V. G. Palchikov, JETP Lett. 122, 144 (2025)], is not due to a new physical effect but is consequence of the asymmetry. To do this, the following model is considered. The phase of a monochromatic optical field is harmonically modulated at the frequency corresponding to the interval between ground-state levels of the Λ-scheme. The carrier is tuned to the low-frequency transition, while the first-order sideband is resonant to the high-frequency transition. I present curves demonstrating the opposite asymmetry of the resonance for the cases of the shift deviating from the light one in different directions.